given a 30 60 90 triangle with an area of 2 sq units. find the
value of the shorter leg.

Answer:

i have the same question brainly peeps help out

Step-by-step explanation:

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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The point (x,y) = (-1.5) is in the second quadrant. So the best way is to draw a point in the xy coordinate plane and a line segment at the origin (0,0).

Now draw a line from (-1.5) to the x-axis. What you should have is a right triangle with the following coordinates: (0,0); (-1.5); (-1.0).

If you look at a right triangle, it has a small leg on the x-axis. Its length is 1 unit. The larger leg is 5 units long. The length of the hypotenuse can be calculated using the Pythagorean theorem. c2 = a2 + b2, the length of hypotenuse c is √26.

In summary,

- length of short leg = 1 unit

- length of long leg = 5 units

- length of hypotenuse = √26 units

Let x be the length of the leg on the x axis (short leg). Let

y be the length of the other leg (long leg).

Let r be the length of the hypotenuse.

x = -1

y = 5

r = √26

Now we can calculate the trigonometric identity:

sin θ = y/r

cos θ = x/r

tan θ = y/x

cot θ = x/y

seconds θ = r/x

csc θ = r/y

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8449

Answer:

3x=2y
Explanation:

There is a proportional relationship between the number of apples and  teaspoons of cinnamon that is 3x = 2y.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given that Devon’s favorite apple sauce recipe calls for 2 teaspoons of cinnamon for every 3 apples.

Now, let x be the number of apple and y be the teaspoons of cinnamon

the proportion are;

x/2 = y/3

Therefore, the proportional relationship between the number of apples and  teaspoons of cinnamon is

3x=2y

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The associative property states that the way in which two or more terms are grouped in a sum does not affect the value. In other words, changing the grouping of terms within a sum does not change the result or total value of the expression.

For addition, the associative property can be expressed as (a + b) + c = a + (b + c), where a, b, and c are any real numbers. This property holds true regardless of the values of a, b, and c.

To understand this concept, let's consider an example. Let's say we have the expression (2 + 3) + 4. According to the associative property, we can group the terms in different ways without changing the result. We can group the terms as (2 + 3) + 4 or as 2 + (3 + 4).

If we evaluate the expression using the first grouping, we add 2 and 3 to get 5, and then add 5 and 4 to get 9. Similarly, if we evaluate the expression using the second grouping, we add 3 and 4 to get 7, and then add 2 and 7 to get 9.

As we can see, regardless of how we group the terms, the result is the same. The value does not change. This is the essence of the associative property.

The associative property is a fundamental property in mathematics and is applicable to various operations, including addition and multiplication. It allows us to rearrange terms within an expression without altering the overall value, providing flexibility and convenience in mathematical calculations and simplifications.

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The given answer is incorrect as it incorrectly factors the numerator and includes additional terms. The correct factorization involves factoring out -16t from the numerator and simplifying the expression accordingly.

The given expression involves factoring the numerator, specifically v(2) = lim t→2 \((52t-16t^2) - 40 t- 2\). However, the resulting factorization provided in the answer is incorrect: -16t should be factored out instead of 52. Additionally, the terms t − 40 and t − 2 should not be present in the factorization. Therefore, the answer given is incorrect.

To find the correct factorization, we need to rearrange the expression. Starting with v(2) = lim t→2  \((52t-16t^2) - 40 t- 2\), we can factor out a common factor of -16t from the numerator. This gives us v(2) = lim t→2 -16t(4 - 13t) - 40 t - 2. Simplifying further, we obtain v(2) = lim t→2 -16t(13t - 4) - 40 t - 2. It is important to carefully follow the rules of factoring and simplify each term to correctly obtain the factorization.

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Answer:

x>-4

Step-by-step explanation:

3[2x+7]+7>4

6x+21+7>4. (3×2x&3×7)

6x+28>4

6x>4-28

6x>-24

x>-24/6

x>-4

The steps in Mia's method were smaller than in Jenna's, which was an advantage.

The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.

The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.

Jenna's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}\)

Mia's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}\)

Both used the right approach, albeit in different ways.

One uses the distributive property, whereas the other uses direct calculation.

Consequently, Jenna and Mia came to the same conclusion.

However, Mia's approach has one advantage over Jenna's: it requires fewer steps.

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This distance of 8.66 centimeters is the maximum separation of the tips of the hour and minute hands of an analog clock over a 24 hour period.

The distance between the two tips of the hands of an analog clock can be calculated with the Pythagorean Theorem. The difference in time between the two hands is 1 hour, or 15 degrees

1. Calculate the angle between the two hands:

1 hour = 15 degrees

2. Calculate the hypotenuse of the triangle formed by the two hands:

3 cm and 4 cm = 5 cm

3. Calculate the distance between the two tips using the cosine of the angle:

5 cm x 1.73= 8.66 cm

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First blank: Substitution or transitive property of equality

Second blank: Subtraction property of equality

The limit of f(x) as x approaches 3 from the left is undefined. This is because the function f(x) is not defined for values of x less than 3.

In the given function, f(x) takes different forms depending on the value of x. For x values between 0 and 3, f(x) is defined as the square root of (9 - x^2). However, as x approaches 3 from the left, the function is not defined for x values less than 3.

Therefore, we cannot determine the value of f(x) as x approaches 3 from the left.

In summary, the limit of f(x) as x approaches 3 from the left is undefined because the function is not defined for values of x less than 3.

This means that we cannot determine the value of f(x) as x approaches 3 from the left because it is not specified in the given function.

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The area A burned as a function of time, t is

A(t)=78.5t²+62.8t+12.56

A circle's or sphere's radius is any of the line segments that connect the object's center to its perimeter; in more recent usage, it is also their length.

According to the given values ;

r(t)=5t+2

.°. A(t)=πr²=π*(5t+2)²

        =π(25t²+20t+4)

        = 78.5t²+62.8t+12.56

hence ,the area A burned as a function of time, t is

A(t)=78.5t²+62.8t+12.56

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Answer: 85.25

Step-by-step explanation:

You find the litres of petrol you want and go up until you find where the line crosses this point and then see how far you can travel on the left so

a is 15km

and b is 39km

Answer:

12 lemons

Step-by-step explanation:

CP of 15 lemon = ₹ 1

Profit = 25 %

SP of 15 lemons = \(\frac{100+profit}{100}*CP\)

    \(= \frac{125}{100}*1\\\\= \frac{5}{4}\)

SP of 15 lemons =  ₹  \(\frac{5}{4}\)

Number of lemon for  ₹  \(\frac{5}{4}\)  = 15

Number of lemons for  ₹  1 = 15 ÷ \(\frac{5}{4}\)

                                            \(= 15 *\frac{4}{5}\\\\= 3*4\\\\= 12\)

To estimate the proportion of students who never read the text, the confidence level used is 95% or higher.

true population parameter. The confidence level of a confidence interval determines the probability that the confidence interval includes the true population parameter.

confidence interval and vice versa.What is proportion, The proportion is a type of variable that records the fraction of the sample or population that has a specific characteristic or answer.

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Answer:

Step-by-step explanation:

\(\frac{8}{2x} =\frac{x}{6} \\2x^{2} =8 \times 6\\x^{2} =24\\x= \pm 2\sqrt{3} \\BD=2 \sqrt{3}\\FG=2 *2 \sqrt{3}=4\sqrt{3}\)

Answer: I belive it’s C sorry if it’s wrong

Step-by-step explanation: because if you rotate it it will swap sides making it A,B

The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. \(f(x)=a(x-h)^2+k, where (h,k)\) is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a\(x^2\) is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

\(a(x+\frac{b}{2a} )^2\) This is a horizontal shift of magnitude |\(\frac{b}{2a}\)| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |\(\frac{D}{4a}\)| units. The direction of the shift will be decided by the sign of \(\frac{D}{4a}\). The final vertex of the parabola will be at (\(\frac{-b}{2a} ,\frac{-D}{4a}\)).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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The product of three consecutive positive integers is always divisible by 6.

We can prove this statement using mathematical induction. The statement we want to prove is that the product of three consecutive positive integers is divisible by 6. To do this, we will use the induction hypothesis:

Let P(n) be the statement: The product of three consecutive positive integers starting with n is divisible by 6.

We will prove that P(n) is true for all natural numbers n.

Base Case: Let n = 1. Then the product of the three consecutive positive integers (1, 2, 3) is 6, which is divisible by 6. Therefore, P(1) is true.

Inductive Step: Assume that P(k) is true, where k is any natural number. We will now prove that P(k + 1) is also true.

The three consecutive positive integers starting with k + 1 are k + 1, k + 2, and k + 3. We can then rewrite the product of these three consecutive positive integers as follows:

(k + 1)(k + 2)(k + 3) = k3 + 3k2 + 6k + 6.

Since we assumed that P(k) is true, we know that k3 + 3k2 + 6k is divisible by 6. Therefore, the entire expression k3 + 3k2 + 6k + 6 is also divisible by 6. Since 6 is also added to this expression, we know that the product of three consecutive positive integers starting with k + 1 is divisible by 6. Therefore, P(k + 1) is true.

Since we have proven the base case and the inductive step, we have proven the statement for all natural numbers n. Therefore, the product of three consecutive positive integers is always divisible by 6.

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Answer:

19, 22.5, 26, 29.5

Step-by-step explanation:

i believe it's going up by 3.5 each time.

Answer:

35.5

Step-by-step explanation:

31+29+33+37+43+38+33+40

=284

284 ÷8 ( how many numbers there are)

=35.5

x<4 is the solution of the inequality 5 x < 20

A number system is defined as a system of writing to express numbers.

The given inequality is  5 x < 20

We have to solve for x

Divide both sides by 5

x<20/5

Divide numerator and denominator by 5

x<4

The graph of x<4 is given in the attachment.

Hence, x<4 is the solution of the inequality 5 x < 20

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The answer for the given Laplace Transform, f(s), is e^(-s)[(1/s^2) - (1/s)].

To find f(s), we can start by applying the Laplace transform to the given function:
ℒ{(t − 1)(t − 1)} = ℒ{t^2 - 2t + 1} = 1/s^3 - 2/s^2 + 1/s


Identify the function
We have the function (t - 1)u(t - 1), where u(t - 1) is the unit step function.

Apply the Laplace Transform property for the unit step function
The Laplace Transform of u(t - a)f(t - a) is given by e^(-as)F(s), where a = 1 in our case. So, we need to find the Laplace Transform of f(t - a) = f(t - 1).

Find the Laplace Transform of f(t - 1)
Our function f(t - 1) = t - 1. The Laplace Transform of t^n is given by n!/(s^(n+1)), so for n = 1, the Laplace Transform of t is 1!/(s^2) = 1/s^2. Since we have t - 1, we find the Laplace Transform of the constant 1 as well, which is 1/s.

So, the Laplace Transform of f(t - 1) = (1/s^2) - (1/s).

Apply the Laplace Transform property
Now, we apply the e^(-as)F(s) property with a = 1:
f(s) = e^(-s)[(1/s^2) - (1/s)]

So, the answer for the given Laplace Transform, f(s), is e^(-s)[(1/s^2) - (1/s)].

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Answer:

7

Step-by-step explanation:

Answer:

4 and 1

Step-by-step explanation:

theyre beside each other

Answer:

1:30

Step-by-step explanation:

($97.50 - $60) divided by $12.50

     37.50 divided by $12.50 = 3

 3 hours + 10:30 = 1:30

In the XY plane, the circles with equations (x-3) + y = 11 and (x+2) + y = r are externally tangent. the value of r is -6.

Generally, To find the value of r, we can start by solving for the centers and radii of the two circles.

The equation of the first circle is of the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. We can rewrite the equation of the first circle as (x - 3)² + y² = 11², so the center of the circle is (3, 0) and the radius is 11.

The equation of the second circle is also of the form (x - h)₂ + (y - k)₂ = r². We can rewrite the equation of the second circle as (x + 2)² + y² = r², so the center of the circle is (-2, 0) and the radius is r.

Since the two circles are externally tangent, the distance between their centers is equal to the sum of their radii. Therefore, the distance between the centers is equal to 11 + r. We can use the distance formula to find the distance between the centers:

distance = √((h₂ - h₁)^2 + (k₂ - k₁)²)

Plugging in the coordinates of the centers, we get:

distance = √((-2 - 3)^2 + (0 - 0)^2) = √(5^2 + 0^2) = √(25) = 5

Since the distance between the centers is equal to the sum of the radii, we can set up the equation:

5 = 11 + r

Solving for r, we get:

r = 5 - 11 = -6

Therefore, the value of r is -6.

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Answer:

True

Step-by-step explanation:

This is one to one relation, therefore it is a function